Abstract
The Chermak–Delgado lattice of a finite group [Formula: see text] is a sublattice of the subgroup lattice of [Formula: see text] that has attracted interest since its discovery. In this paper, we show that every subgroup of [Formula: see text] in the Chermak–Delgado lattice is subnormal in [Formula: see text] with subnormal depth bounded by both the depth and height function of the Chermak–Delgado lattice; we provide a nontrivial example showing that our bounds are sharp. We also show that determining whether a given subgroup [Formula: see text] is in the Chermak–Delgado lattice can be decided by examining only those subgroups of [Formula: see text] that are comparable with [Formula: see text].
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